## More Homework 3

Everything about Sudoku that doesn't fit in one of the other sections

### Re: More Homework 3

A
Code: Select all
` . . . . . . . 2 3 . 1 . . . . 4 . . . . . 1 . . 7 8 . 1 . . 2 7 5 . . . . . . . . 6 . 1 . . . . 9 . 4 . . . 2 . . . 8 . . 7 . . . 6 . . . . . 5 8 4 . . . 9 . . .  23C`

m_b_metcalf
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### Re: More Homework 3

coloin wrote:B
Code: Select all
`+---+---+---+|...|...|..9||.1.|...|4..||...|1..|8.3|+---+---+---+|1..|...|6..||...|71.|98.||...|...|24.|+---+---+---+|92.|.6.|...||.45|.92|...||3..|..4|...|+---+---+---+   23 clues .... but cant get rid of the interlopping clue !`

I suspect that B is either impossible or is extremly rare (I found no valid puzzle in 500,000 tries).

Mike

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### Re: More Homework 3

Code: Select all
`A+---+---+---+|...|...|.6.||.1.|...|...||...|1..|983|+---+---+---+|1..|.3.|...||...|5.6|1..||...|.7.|...|+---+---+---+|6.9|..2|4..||..3|...|..8||.2.|.5.|7..|+---+---+---+   21C`

I suspect that B is either impossible or is extremly rare

I agree.

JPF
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### Re: More Homework 3

Therefore ..... In the style of JPF
Code: Select all
`+---+---+---+|1..|...|234||...|...|561||...|1..|789|+---+---+---+|..1|...|893||...|...|172||...|...|456|+---+---+---+|425|368|917||768|291|345||319|754|628|+---+---+---+    43 sols`
coloin

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### Re: More Homework 3

B
Code: Select all
` . . . . . . 1 9 7 . 1 . . . . 3 8 4 . . . 1 . . 6 2 5 1 . . . . . 4 6 2 . . . . 1 . 5 7 9 . . . . . . 8 1 3 6 8 4 2 3 7 9 5 1 2 3 1 6 9 5 7 4 8 5 7 9 4 8 1 2 3 6   4 solutions `

m_b_metcalf
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### Re: More Homework 3

Code: Select all
`A+---+---+---+|...|...|.9.||.1.|...|...||...|1..|582|+---+---+---+|1..|...|...||...|263|1..||...|.7.|...|+---+---+---+|8.9|..4|...||..3|..7|.5.||.2.|...|7..|+---+---+---+    20C`

JPF
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### Re: More Homework 3

m_b_metcalf wrote:I suspect that B is either impossible or is extremly rare (I found no valid puzzle in 500,000 tries).Mike

yes I think its impossible as its unlikely with r3c4 = r4c3 it will ever be valid

Code: Select all
`+---+---+---+|...|...|123||...|...|456||...|1..|789|+---+---+---+|..1|...|932||...|...|547||...|...|861|+---+---+---+|629|875|314||453|961|278||178|243|695|+---+---+---+    best was 7 solutions !`

the 1@r2c2 and the1@r5c5 are placed
coloin

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### Re: More Homework 3

B
Code: Select all
` . . . . . . 3 9 1 . 1 . . . . 2 8 6 . . . 1 . . 4 5 7 1 . . . . . 5 3 4 . . . . 1 . 6 2 9 . . . . . . 1 7 8 7 9 3 5 4 6 8 1 2 5 8 6 7 2 1 9 4 3 4 2 1 3 8 9 7 6 5  5 solutions`

These low solution counts (<6) occur at a rate of less than one per million.

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### Re: More Homework 3

m_b_metcalf wrote:B
Code: Select all
`+---+---+---+|...|...|197||.1.|...|384||...|1..|625|+---+---+---+|1..|...|462||...|.1.|579||...|...|813|+---+---+---+|684|237|951||231|695|748||579|481|236|+---+---+---+   4 solutions`

Unless we're mistaken, I agree with Mike: the minimum number of solutions is 4.
The corollary question is now: How many cells can be placed?
In Mike's example, the number of placed cells is 16 (65-49)
Code: Select all
`+---+---+---+|..5|.4.|197||71.|5.9|384||94.|17.|625|+---+---+---+|19.|75.|462||...|.14|579||457|9..|813|+---+---+---+|684|237|951||231|695|748||579|481|236|+---+---+---+`

What are the lowest and the greatest number of cells that can be placed?

JPF
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### Re: More Homework 3

JPF wrote:Unless we're mistaken...

No you are not mistaken ... it looks like all 4 boxes that are solved with 2 clues have different 2 clues
if there was one [4box] which solved with 2 siimilar clues there would be 10000 or more examples ... eg a random B1247 has many solutions
Code: Select all
`+---+---+---+|123|456|789||784|291|...||659|387|...|+---+---+---+|462|175|...||391|824|...||578|963|...|+---+---+---+|2..|...|...||9..|...|...||8..|...|...|+---+---+---+  over 10000 solutions`

In terms of crossing gangsters ..... dukuso posted that "there are essentially 2802 different [B1]B2B3B4B7" { these share the same 3-tuples ] [althougfh ED count is perhaps ~15 million]

Ive only looked at a few of these - but in general its usually possible to solve a B12347 with plus 3 clues in the 4-boxes. [ min is 2 and probably all can be solved in 4]

The ED count of the 4-boxes is ~ 10 million I believe bit I dont know how many actual 4-boxes are solvable with 2 [different] clues.
Code: Select all
`+---+---+---+|8..|...|675||...|...|928||...|...|341|+---+---+---+|...|9..|237||...|...|594||...|...|816|+---+---+---+|123|456|789||598|721|463||647|398|152|+---+---+---+             +---+---+---+|839|142|...||714|563|...||256|879|...|+---+---+---+|461|985|...||382|617|...||975|234|...|+---+---+---+|...|...|...||...|...|...||...|...|...|+---+---+---+`

For a specific 4 box - probably the maximum number of UAs that I can fit is 4 plus big one
Code: Select all
`+---+---+---+                              |12.|.78|...|                              |3..|4..|...|                              |4..|3..|...|                              +---+---+---+                              |215|..6|...|                              |..6|..5|...|                              |...|.87|...|                              +---+---+---+                              |...|...|...|                              |...|...|...|                              |...|...|...|                              +---+---+---+  4 UA4s plus ? a big one                                                +---+---+---+                              |129|578|...|                              |367|421|...|                              |458|369|...|                              +---+---+---+                              |215|946|...|                              |786|135|...|                              |934|287|...|                              +---+---+---+                              |...|...|...|                              |...|...|...|                              |...|...|...|                              +---+---+---+    so probably 5 clues needed`
coloin

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### Re: More Homework 3

JPF wrote:What are the lowest and the greatest number of cells that can be placed?
JPF

Hmmm i dont think mike's effort is going to be bettered ...

but I guess this might be the next one to look at
Code: Select all
`+---+---+---+|1..|...|.34||...|1..|567||...|...|.89|+---+---+---+|.1.|.34|...||...|567|...||...|89.|.2.|+---+---+---+|.34|...|...||79.|..2|...||865|...|..2|+---+---+---+    705 sols`

Is there is a grid with 1 solution - if so we can find the minum clues.....
coloin

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### Re: More Homework 3

Hmmm i dont think mike's effort is going to be bettered ...

Actually, it can...
Is there is a grid with 1 solution..

Code: Select all
`+---+---+---+|1..|...|.89||...|1..|6.5||...|...|.73|+---+---+---+|.1.|3..|...||...|4.7|...||...|658|.2.|+---+---+---+|4..|...|...||6.3|..2|...||.79|...|..2|+---+---+---+    23C`

Edit:
Code: Select all
`+---+---+---+|1..|...|..5||...|1..|7.3||...|...|.98|+---+---+---+|.1.|3..|...||...|4.7|...||...|869|.2.|+---+---+---+|3..|...|...||4.6|..2|...||.89|...|..2|+---+---+---+   22C`

JPF
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### Re: More Homework 3

JPF wrote:What are the lowest and the greatest number of cells that can be placed?

Here are two candidates for the lowest number of cells that can be placed:
Code: Select all
`Common clues (51): . . . . 6 . 3 9 1 . 1 . . . . 2 8 6 . . . 1 . . 4 5 7 1 . . . . . 5 3 4 . . . . 1 . 6 2 9 . . 9 . . . 1 7 8 7 9 3 5 4 6 8 1 2 5 8 6 7 2 1 9 4 3 4 2 1 3 8 9 7 6 5  5 solutions, 2 placedCommon clues (52): . . . . . 2 8 1 4 . 1 . . . . 2 5 9 . . . 1 . . 6 3 7 1 . . . . . 7 6 8 . . . . 1 . 4 9 5 . . 4 . . 8 3 2 1 6 2 1 7 4 9 5 8 3 7 5 8 3 2 1 9 4 6 3 4 9 8 5 6 1 7 2  4 solutions, 3 placed`

JPF wrote:
Hmmm i dont think mike's effort is going to be bettered ...

Actually, it can...

JPF

I haven't understood Are we still talking about B?

m_b_metcalf
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### Re: More Homework 3

I was speaking about B having 4 solutions...

JPF
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### Re: More Homework 3

JPF wrote:Unless we're mistaken, I agree with Mike: the minimum number of solutions is 4.
The corollary question is now: How many cells can be placed?
In Mike's example, the number of placed cells is 16 (65-49)
[snip]
What are the lowest and the greatest number of cells that can be placed?

I suppose you mean for 4-solutions B grids. For many-solution grids I get:
Code: Select all
` . . . . . . 8 1 5 . 1 . . . . 6 2 7 . . . 1 . . 3 9 4 1 . . . . . 9 5 2 . . . . 1 . 4 7 8 . . . . . . 1 3 6 7 3 8 6 5 1 2 4 9 5 4 9 8 3 2 7 6 1 2 6 1 4 7 9 5 8 3  49 clues, many solutions, none placed 9 5 . . 6 . 7 8 1 8 1 6 5 9 7 2 4 3 . 7 . 1 8 . 5 6 9 1 9 . . 7 . 6 5 8 . 8 5 . 1 6 4 9 7 4 6 7 8 5 9 3 1 2 5 3 1 6 2 8 9 7 4 7 2 8 9 4 5 1 3 6 6 4 9 7 3 1 8 2 5  70 clues, 4 solutions, 21 placed`

I look forward to seeing your 2(?)-solutions B grid!

Mike

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